(10) Let X(t) = 13e-¹ + 2(1 − e¯¹) + Selª~¹dW(s). What is the SDE for X(t)? [Hint: Consider Y(t) = e'X(t) — X(0), and obtain its SDE first. Then apply Ito to X(t) = f(t, Y(t)) for an appropriate f.] The following answers are proposed. (a) dx = (2- X(t))dt + 2dW, X(0) = 13 (b) dx = (2 - X(t))dt + dW.X(0) = 1 (c) dx = (13- X(t))dt+dW, X(0) = 2 (d) dx = (2- X(t))dt+dW, X(0) = 13 (e) None of the above is correct Choose the best answer. (h) (c)
(10) Let X(t) = 13e-¹ + 2(1 − e¯¹) + Selª~¹dW(s). What is the SDE for X(t)? [Hint: Consider Y(t) = e'X(t) — X(0), and obtain its SDE first. Then apply Ito to X(t) = f(t, Y(t)) for an appropriate f.] The following answers are proposed. (a) dx = (2- X(t))dt + 2dW, X(0) = 13 (b) dx = (2 - X(t))dt + dW.X(0) = 1 (c) dx = (13- X(t))dt+dW, X(0) = 2 (d) dx = (2- X(t))dt+dW, X(0) = 13 (e) None of the above is correct Choose the best answer. (h) (c)
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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![(10) Let X(t) = 13e-¹ + 2(1 −e¯¹) + Seªt) dW(s). What is the SDE for X(t)? [Hint: Consider Y(t) = e¹X(t) — X(0), and obtain its SDE first. Then apply Ito to X(t) = f(t, Y(t)) for an appropriate f.]
The following answers are proposed.
(a) dx = (2- X(t))dt + 2dW, X(0) = 13
(b) dx = (2- X(t))dt + dW, X(0) = 1
(c) dx = (13 - X(t))dt + dW, X(0) = 2
(d) dX = (2 — X(t))dt + dW, X(0) = 13
(e) None of the above is correct
Choose the best answer.
(Select One)
(a)
(b)
o
(c)
O
(d)
O
(e)
O
N/A](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F546ca3ef-5c41-4b6f-8ba8-1af4930ff657%2F757273e7-6cb1-4919-b0d6-26bcbab89e08%2Fioj77a_processed.png&w=3840&q=75)
Transcribed Image Text:(10) Let X(t) = 13e-¹ + 2(1 −e¯¹) + Seªt) dW(s). What is the SDE for X(t)? [Hint: Consider Y(t) = e¹X(t) — X(0), and obtain its SDE first. Then apply Ito to X(t) = f(t, Y(t)) for an appropriate f.]
The following answers are proposed.
(a) dx = (2- X(t))dt + 2dW, X(0) = 13
(b) dx = (2- X(t))dt + dW, X(0) = 1
(c) dx = (13 - X(t))dt + dW, X(0) = 2
(d) dX = (2 — X(t))dt + dW, X(0) = 13
(e) None of the above is correct
Choose the best answer.
(Select One)
(a)
(b)
o
(c)
O
(d)
O
(e)
O
N/A
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